A value of \( \theta \in(0, \pi / 3) \), for which \( \left|\begin{array}{ccc}1+\cos ^{2} \theta...

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A value of \( \theta \in(0, \pi / 3) \), for which \( \left|\begin{array}{ccc}1+\cos ^{2} \theta & \sin ^{2} \theta & 4 \cos 6 \theta \\ \cos ^{2} \theta & 1+\sin ^{2} \theta & 4 \cos 6 \theta \\ \cos ^{2} \theta & \sin ^{2} \theta & 1+4 \cos 6 \theta\end{array}\right|=0 \)    is
(a) \( \frac{\pi}{9} \)
(b) \( \frac{\pi}{18} \)
(c) \( \frac{7 \pi}{24} \)
(d) \( \frac{7 \pi}{36} \)
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